Thanks for your contributions, tomleslie and mmcdara. I haven't had so much time to investigate things today.
tomlesIie, I will look into your way of handling the model solution in a matrix. Also thanks for the events option, which I didn't know beforehand.
mmcdara, your way of handling the problem is very advanced and impressing, and you say you are not even finished :) I went through your code, and could understand part of it - in the time I had available today. I perfectly understand your idea of trying to find an estimate for the parameters alpha (the initial angle), v__0 (the initial velocity) and the Drag coefficient each contain an error. My original values were not the best. I had two few data points at the beginning of the throw to be able to give a value for alpha and v__0 with a high precision. Unfortunately only a minor deviation from the 'true' value vill result in quite large deviation in the throw-length, I am sure (so sensitive on the parameters). Therefore I think one need somehow to estimate these, and not take my original values for granted. Also probably the Drag Coefficient isn't as precise as desirable, although the weight of the ball is very precise as well as the diameter (the formula for the Drag Coefficient is in it's own a model ...). But wouldn't it be possible to use the experimental data to make the estimate, or is that cheating? I attach a zip-file containing four files: A new updated Maple file, in which I have imported the columns from the Excel file containing the experimental data, the Excel-file itself as well as two screenshots. One screenshot display a frame from the video, which will eventually give an idea about the precision. The other screenshot are the data-points plotted in a graph.
NB! Remark that my new Maple file have slightly other values for the constants compared to my first Maple file. I wasn't able to find my original data-file for the first experiment, so I now use data from another one and adjusted the parameters. It should be no big deal though. The new constants can be substituted and the Maple file re-executed ...
So my question has now more shifted towards: what is the most proper way to evaluate or decide if model 2 is a good model for the experimental data? Although I feel very tempted to learn more about the Bayesian way myself (it is probably the best way) I hope there is a shorter way, because my students will never understand it. Would it be possible to use the command LSSolve from the Optimization package?
Thanks a lot for the contributions. This debate has turned into a very interesting one ...